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Cambridge-Duisenberg/Tinbergen annual exchange, Amsterdam, Netherlands, 23rd May 2014

Cambridge-Duisenberg/Tinbergen annual exchange, Amsterdam, Netherlands, 23rd May 2014

Cambridge Speakers  for 23 May 2014

Ben Derrett (StatsLab)

Title: Continuously-­‐generated Jump Processes: A framework for efficient pricing with jumps and stochastic volatility

 Abstract: We construct a flexible and numerically tractable class of asset models by firstly choosing a bivariate diffusion process $(X,Y)$, and then defining the price of the asset at time $t$ to be the value of $Y$ when $X$ first exceeds $t$. Such price processes will typically have jumps; conventional pricing methodologies would try to solve a PIDE, which can be numerically problematic, but using the fact that the pricing problem is embedded in a two-­‐ dimensional diffusion, we are able to exploit efficient methods for two-­‐dimensional diffusion equations to find prices. Models with time dependence (that is, where the bivariate diffusion is $X$-­‐dependent) are no more difficult in this approach. Pricing a European option for a model in this class consists of solving a second order elliptic PDE. This problem is amenable to highly optimized and robust numerical PDE solving techniques such as adaptive meshing, solution error estimates and the finite element approach.

 Models in this class range from the most parsimonious, with few parameters, to those which can match the observed term structure of implied volatility. This allows flexibility. We construct an example model which accounts for so-­‐called volatility events, caused by the scheduled release of pertinent information, such as unemployment figures, inflation rates and economic growth rates. Finally, we discuss the computation of parameter sensitivities and calibration of models in this class.

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Andrew Harvey and Rutger-­Jan Lange (Economics)

Title: On the Formulation of ARCH in Mean Models

Abstract: Volatility of a stock may incur a risk premium, leading to a positive correlation between volatility and returns. On the other hand the leverage e¤ect, whereby negative returns increase volatility, acts in the opposite direction. We propose a two component ARCH in Mean model to separate the two e¤ects. Our exponential formulation, with the dynamics driven by the score of the conditional distribution, is shown to be theoretically tractable as well as practically useful. In particular we solve the problem of obtaining the asymptotic distrib-­‐ ution of the maximum likelihood estimator, something that has not proved possible for standard formulations of ARCH in Mean. Keywords: Dynamic conditional score model; returns ; risk premium; score; t-­‐distribution; two component model; volatility

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M A H Dempster (Centre for Financial Research, University of Cambridge & Cambridge Systems Associates)

Title: THE TRUE COST OF OTC DERIVATIVES

Abstract: Since the breakdown in the early 70's of the postwar Bretton Woods fixed exchange rates and the achievements of Black, Scholes and Merton in obtaining a satisfactory theory of option pricing almost simultaneously, banking globally has undergone sweeping transformations at an ever increasing pace. After briefly surveying financial market developments from 1980 to the present, the role of structured over-­‐the-­‐counter derivatives in this advance will be examined in some detail. Previous extensive technical consultancy to leading banks on structured derivative products has been followed since the crisis by expert witness work for clients -­‐-­‐   individual, commercial and governmental -­‐-­‐   who have purchased these OTC products to their cost. This recent and ongoing experience has been an eye opener which I shall detail with numerous real examples. The presentation will go on to discuss our pricing methodology for these examples and close with comments on the evolving global regulation of structured OTC derivatives.

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